Chapter 11
Events, Qualities, Quantities, And Other Vague Words: On Lojban Abstraction

1. The syntax of abstraction

The purpose of the feature of Lojban known as ``abstraction'' is to provide a means for taking whole bridi and packaging them up, as it were, into simple selbri. Syntactically, abstractions are very simple and uniform; semantically, they are rich and complex, with few features in common between one variety of abstraction and another. We will begin by discussing syntax without regard to semantics; as a result, the notion of abstraction may seem unmotivated at first. Bear with this difficulty until Section 2.

An abstraction selbri is formed by taking a full bridi and preceding it by any cmavo of selma'o NU. There are twelve such cmavo; they are known as ``abstractors''. The bridi is closed by the elidable terminator ``kei'', of selma'o KEI. Thus, to change the bridi

1.1)  mi klama le zarci
    I go-to the store

1.2)  nu mi klama le zarci [kei]
    an-event-of my going-to the store

(Technically, ``kei'' is never necessary, because the elidable terminator ``vau'' that closes every bridi can substitute for it; however, ``kei'' is specific to abstractions, and using it is almost always clearer.)

The grammatical uses of an abstraction selbri are exactly the same as those of a simple brivla. In particular, abstraction selbri may be used as observatives, as in Example 1.2, or used in tanru:

1.3)  la djan. cu nu sonci kei djica
    John is-an-(event-of being-a-soldier) type-of desirer.
    John wants to be a soldier.

1.4)  la djan. cu djica le nu sonci [kei]
    John desires the event-of being-a-soldier.

We will most often use descriptions containing abstraction either at the end of a bridi, or just before the main selbri with its ``cu''; in either of these circumstances, ``kei'' can normally be elided.

The place structure of an abstraction selbri depends on the particular abstractor, and will be explained individually in the following sections.

Note: In glosses of bridi within abstractions, the grammatical form used in the English changes. Thus, in the gloss of Example 1.2 we see ``my going-to the store'' rather than ``I go-to the store''; likewise, in the glosses of Example 1.3 and Example 1.4 we see ``being-a-soldier'' rather than ``is-a-soldier''. This procedure reflects the desire for more understandable glosses, and does not indicate any change in the Lojban form. A bridi is a bridi, and undergoes no change when it is used as part of an abstraction selbri.

2. Event abstraction

   nu  NU  event abstractor

2.1)  le klama
    the comer, that which comes

2.2)   le se klama
    the destination

2.3)   le te klama
    the origin

2.4)   le ve klama
    the route

2.5)   le xe klama
    the means of transportation

2.6)   le nu klama
    the event of someone coming to somewhere
        from somewhere by some route using some means

In Lojban, the term ``event'' is divorced from its ordinary English sense of something that happens over a short period of time. The description:

2.7)  le nu mi vasxu
    the event-of my breathing

2.8)  le nu la djan. cinba la djein.
    the event-of John kissing Jane

We can see from Examples 2.6 through 2.8 that ellipsis of sumti is valid in the bridi of abstraction selbri, just as in the main bridi of a sentence. Any sumti may be ellipsized if the listener will be able to figure out from context what the proper value of it is, or else to recognize that the proper value is unimportant. It is extremely common for ``nu'' abstractions in descriptions to have the x1 place ellipsized:

2.9)  mi nelci le nu limna
    I like the event-of swimming.
    I like swimming.

2.10)    mi nelci le nu mi limna
    I like the event-of I swim.

In the proper context, of course, Example 2.9 could refer to the event of somebody else swimming. Its English equivalent, ``I like swimming'', can't be interpreted as ``I like Frank's swimming''; this is a fundamental distinction between English and Lojban. In Lojban, an omitted sumti can mean whatever the context indicates that it should mean.

Note that the lack of an explicit NU cmavo in a sumti can sometimes hide an implicit abstraction. In the context of Example 2.10, the appearance of ``le se nelci'' (``that which is liked'') is in effect an abstraction:

2.11)    le se nelci cu cafne
    The liked-thing is-frequent.
    The thing which I like happens often.

My swimming happens often.

Event descriptions with ``le nu'' are commonly used to fill the ``under conditions...'' places, among others, of gismu and lujvo place structures:

2.12)    la lojban. cu frili mi
        le nu mi tadni [kei]
    Lojban is-easy for-me
        under-conditions-the event-of I study
    Lojban is easy for me when I study.

The place structure of a ``nu'' abstraction selbri is simply:

x1 is an event of (the bridi)

3. Types of event abstractions

   mu'e    NU  point-event abstractor
    pu'u    NU  process abstractor
    zu'o    NU  activity abstractor
    za'i    NU  state abstractor

3.1)  le mu'e la djan. catra la djim. cu zekri
    the point-event-of (John kills Jim) is-a-crime
    John's killing Jim (considered as a point in time)
        is a crime.

3.2)  ca'o le pu'u le latmo balje'a
        cu porpi kei
        so'i je'atru cu selcatra
    [continuitive] the process-of( the Latin great-state
        breaking-up )
        many state-rulers were-killed
    During the fall of the Roman Empire,
        many Emperors were killed.

3.3)  mi tatpi ri'a le zu'o mi plipe
    I am-tired because-of the activity-of (I jump)
    I am tired because I jump.

3.4)  le za'i mi jmive cu ckape do
    the state-of (I am-alive) is-dangerous-to you
    My being alive is dangerous to you.

the ``state of running'' begins when the runner starts and ends when the runner stops;

the ``activity of running'' consists of the cycle ``lift leg, step forward, drop leg, lift other leg...'' (each such cycle is a process, but the activity consists in the repetition of the cycle);

the ``process of running'' puts emphasis on the initial sprint, the steady speed, and the final slowdown;

the ``achievement of running'' is most alien to English, but sees the event of running as a single indivisible thing, like ``Pheidippides' run from Marathon to Athens'' (the original marathon).

Further information on types of events can be found in Section 12.

The four event type abstractors have the following place structures:

``mu'e'': x1 is a point event of (the bridi) ``pu'u'': x1 is a process of (the bridi) with stages x2 ``za'i'': x1 is a continuous state of (the bridi) being true ``zu'o'': x1 is an activity of (the bridi) consisting of repeated actions x2

4. Property abstractions

   ka  NU  property abstractor
    ce'u    KOhA    

4.1)  la djan. cu se risna zo'e
    John has-as-heart something-unspecified.
    John has a heart.

4.2)  la djan. cu ckaji
        le ka se risna [zo'e] [kei]
    John has-the-property
        the property-of having-as-heart something.
    John has the property of having a heart.

Property descriptions, like event descriptions, are often wanted to fill places in brivla place structures:

4.3)  do cnino mi
        le ka xunre [kei]
    You are-new to-me
        in-the-quality-of-the property-of being-red.
    You are new to me in redness.

We can also move the property description to the x1 place of Example 4.3, producing:

4.4)  le ka do xunre [kei] cu cnino mi
    The property-of your being-red is-new to me.
    Your redness is new to me.

There are several different properties that can be extracted from a bridi, depending on which place of the bridi is ``understood'' as being specified externally. Thus:

4.5)  ka mi prami [zo'e] [kei]
    a-property-of me loving something-unspecified

4.6)  ka [zo'e] prami mi [kei]
    a-property-of something-unspecified loving me

In particular, sentences like Example 4.7 and Example 4.8 are quite different in meaning:

4.7)  la djan. cu zmadu la djordj. le ka mi prami
    John exceeds George in-the property-of (I love X)
    I love John more than I love George.

4.8)   la djan. cu zmadu la djordj. le ka prami mi
    John exceeds George in the property of (X loves me).
    John loves me more than George loves me.

The ``X'' used in the glosses of Examples 4.7 through 4.8 as a place-holder cannot be represented only by ellipsis in Lojban, because ellipsis means that there must be a specific value that can fill the ellipsis, as mentioned in Section 2. Instead, the cmavo ``ce'u'' of selma'o KOhA is employed when an explicit sumti is wanted. (The form ``X'' will be used in literal translations.)

Therefore, an explicit equivalent of Example 4.7, with no ellipsis, is:

4.9)  la djan. cu zmadu la djordj. le ka mi prami ce'u
    John exceeds George in-the property-of (I love X).

4.10)    la djan. cu zmadu la djordj. le ka ce'u prami mi
    John exceeds George in-the property-of (X loves me).

This convention allows disambiguation of cases like:

4.11)    le ka [zo'e] dunda le xirma [zo'e] [kei]
    the property-of giving the horse

4.12)    le ka ce'u dunda le xirma
        [zo'e] [kei]
    the property-of (X is-a-giver of-the horse
        to someone-unspecified)
    the property of being a giver of the horse

4.13)    le ka [zo'e] dunda
        le xirma ce'u [kei]
    the property-of (someone-unspecified
        is-a-giver of-the horse to X)
    the property of being one to whom the horse is given

It is also possible to have more than one ``ce'u'' in a ``ka'' abstraction, which transforms it from a property abstraction into a relationship abstraction, a resource of the language that has not yet been explored.

The place structure of ``ka'' abstraction selbri is simply:

x1 is a property of (the bridi)

5. Amount abstractions

   ni  NU  amount abstraction

5.1)  le ni le pixra cu blanu [kei]
    the amount-of (the picture being-blue)
    the amount of blueness in the picture

5.2)  le ni la djein. cu mamta [kei]
    the amount-of (Jane being-a-mother)
    the amount of Jane's mother-ness (?)
    the amount of mother-ness in Jane (?)

Semantically, a sumti with ``le ni'' is a number; however, it cannot be treated grammatically as a quantifier in Lojban unless prefixed by the mathematical cmavo ``mo'e'':

5.3)  li pa vu'u mo'e
        le ni le pixra cu blanu [kei]
    the-number 1 minus the-operand
        the amount-of (the picture being-blue)
    1 - B, where B = blueness of the picture

Mathematical Lojban is beyond the scope of this chapter, and is explained more fully in Chapter 18.

There are contexts where either property or amount abstractions make sense, and in such constructions, amount abstractions can make use of ``ce'u'' just like property abstractors. Thus,

5.4)  le pixra cu cenba le ka ce'u blanu [kei]
    the picture varies in-the property-of (X is blue)
    The picture varies in being blue.
    The picture varies in blueness.

5.5)  le pixra cu cenba le ni ce'u blanu [kei]
    the picture varies in-the amount-of (X is blue)
    The picture varies in how blue it is.
    The picture varies in blueness.

Whenever we talk of measurement of an amount, there is some sort of scale, and so the place structure of ``ni'' abstraction selbri is:

x1 is the amount of (the bridi) on scale x2

6. Truth-value abstraction: ``jei''

The ``blueness of the picture'' discussed in Section 5 refers to the measurable amount of blue pigment (or other source of blueness), not to the degree of truth of the claim that blueness is present. That abstraction is expressed in Lojban using ``jei'', which is closely related semantically to ``ni''. In the simplest cases, ``le jei'' produces not a number but a truth value:

6.1)  le jei li re su'i re du li vo [kei]
    the truth-value-of the-number 2 + 2 = the-number 4
    the truth of 2 + 2 being 4

6.2)  le jei li re su'i re du li mu [kei]
    the truth-value-of the-number 2 + 2 = the-number 5
    the truth of 2 + 2 being 5

However, not everything in life (or even in Lojban) is simply true or false. There are shades of gray even in truth value, and ``jei'' is Lojban's mechanism for indicating the shade of grey intended:

6.3)  mi ba jdice le jei
        la djordj. cu zekri gasnu [kei]
    I [future] decide the truth-value of
        (George being-a-(crime doer)).
    I will decide whether George is a criminal.

x1 is the truth value of (the bridi) under epistemology x2

7. Predication/sentence abstraction

   du'u    NU  predication abstraction

7.1)  I know that Frank is a fool.

How's that in Lojban? Let us try:

7.2)  mi djuno le nu la frank. cu bebna [kei]
    I know the event of Frank being a fool.

Try again:

7.3)  mi djuno le jei la frank. cu bebna [kei]
    I know the truth-value of Frank being a fool.

Closer. Example 7.3 says that I know whether or not Frank is a fool, but doesn't say that he is one, as Example 7.1 does. To catch that nuance, we must say:

7.4)  mi djuno le du'u la frank. cu bebna [kei]
    I know the predication that Frank is a fool.

Now we have it. Note that the implied assertion ``Frank is a fool'' is not a property of ``le du'u'' abstraction, but of ``djuno''; we can only know what is in fact true. (As a result, ``djuno'' like ``jei'' has a place for epistemology, which specifies how we know.) Example 7.5 has no such implied assertion:

7.5)  mi kucli le du'u la frank. cu bebna [kei]
    I am curious about whether Frank is a fool.

7.6)  mi kucli le jei la frank. cu bebna [kei]
    I am curious about how true it is
        that Frank is a fool.

x1 is the predication (the bridi), expressed in sentence x2

7.6.5)  la djan. cusku
        le se du'u
            la djordj. klama le zarci [kei]
    John expresses
        the sentence-expressing-that
            George goes-to the store
    John says that George goes to the store.

7.7)  la djan cusku
        lu la djordj. klama le zarci li'u
    John expresses,
        quote, George goes to the store, unquote.
    John says ``George goes to the store''.

``le se du'u'' is much the same as ``lu'e le du'u'', a symbol for the predication, but ``se du'u'' can be used as a selbri, whereas ``lu'e'' is ungrammatical in a selbri. (See Chapter 5 for a discussion of ``lu'e''.)

8. Indirect questions

   kau UI  indirect question marker

8.1)  I know that John went to the store.

8.2)  I know who went to the store.

To express indirect questions in Lojban, we use a ``le du'u'' abstraction, but rather than using a question word like ``who'' (``ma'' in Lojban), we use any word that will fit grammatically and mark it with the suffix particle ``kau''. This cmavo belongs to selma'o UI, so grammatically it can appear anywhere. The simplest Lojban translation of Example 8.2 is therefore:

8.3)  mi djuno le du'u
        makau pu klama le zarci
    I know the predication-of
        X [indirect question] [past] going to the store.

8.4)  mi djuno le du'u
        la djan. kau pu
            klama le zarci
    I know the predication-of/fact-that
        John [indirect question] [past]
            going to the store.
    I know who went to the store, namely John.
    I know that it was John who went to the store.

Using one of the indefinite pro-sumti such as ``ma'', ``zo'e'', or ``da'' does not suggest any particular value.

Why does Lojban require the ``kau'' marker, rather than using ``ma'' as English and Chinese and many other languages do? Because ``ma'' always signals a direct question, and so

8.5)  mi djuno le du'u
        ma pu klama le zarci
    I know the predication-of
        [what sumti?] [past] goes-to the store

8.6)  Who is it that I know goes to the store?

8.7)  mi djuno fi le pu klama be le zarci
    I know about the [past] goer to-the store.
    I know something about the one who went to the store
        (namely, his identity).

8.8)  mi ba zgana le du'u
        la djan. jikau la djordj.
            cu zvati le panka
    I [future] observe the predication-of/fact-that
        John [connective indirect question] George
            is-at the park.
    I will see whether John or George (or both)
        is at the park.

In addition, Example 8.7 is only a loose paraphrase of Example 8.3, because it is left to the listener's insight to realize that what is known about the goer-to-the-store is his identity rather than some other of his attributes.

9. Minor abstraction types

   li'i    NU  experience abstractor
    si'o    NU  concept abstractor
    su'u    NU  general abstractor

9.1)  mi morji le li'i mi verba
    I remember the experience-of (my being-a-child)

9.2)  mi nelci le si'o la lojban. cu mulno
    I enjoy the concept-of Lojban being-complete.

9.3)  ko zgana le su'u
        le ci smacu cu bajra
    you [imperative] observe the abstract-nature-of
        the three mice running
    See how the three mice run!

x1 is the experience of (the bridi) as experienced by x2

x1 is the idea/concept of (the bridi) in the mind of x2

x1 is an abstract nature of (the bridi) of type x2

9.4)  le nu mi klama
    the event-of my going

9.5)  le su'u mi klama kei be lo fasnu
    the abstract-nature-of (my going) of-type an event

9.6)  le su'u la .iecuas. kuctra
        selcatra kei
        be lo sao'rdzifa'a
        ke nalmatma'e sutyterjvi
    the abstract-nature-of (Jesus is-an-intersect-shape
        type-of-killed-one)
        of-type a slope-low-direction
        type-of non-motor-vehicle speed-competition
    The Crucifixion of Jesus Considered As A
        Downhill Bicycle Race

Note the importance of using ``kei'' after ``su'u'' when the x2 of ``su'u'' (or any other abstractor) is being specified; otherwise, the ``be lo'' ends up inside the abstraction bridi.

10. Lojban sumti raising

   tu'a    LAhE    an abstraction involving
    jai JAI abstraction conversion

10.1)    I try to open the door.

10.2)    mi troci le nu
        [mi] gasnu le nu
            le vorme cu karbi'o
    I try the event-of
        (I am-agent-in the event-of
            (the door open-becomes)).

10.3)    I try the door.

10.4)    mi troci tu'a le vorme
    I try some-action-to-do-with the door.

Using ``tu'a'' is a kind of laziness: it makes speaking easier at the possible expense of clarity for the listener. The speaker must be prepared for the listener to respond something like:

10.5)    tu'a le vorme lu'u ki'a
    something-to-do-with the door [terminator] [confusion!]

10.6)    tu'a la djan. cu cafne
    something-to-do-with John frequently-occurs

This must mean that something which John does, or which happens to John, occurs frequently: but without more context there is no way to figure out what. Note that without the ``tu'a'', Example 10.6 would mean that John considered as an event frequently occurs --- in other words, that John has some sort of on-and-off existence! Normally we do not think of people as events in English, but the x1 place of ``cafne'' is an event, and if something that does not seem to be an event is put there, the Lojbanic listener will attempt to construe it as one. (Of course, this analysis assumes that ``djan.'' is the name of a person, and not the name of some event.)

Logically, a counterpart of some sort is needed to ``tu'a'' which transposes an abstract sumti into a concrete one. This is achieved at the selbri level by the cmavo ``jai'' (of selma'o JAI). This cmavo has more than one function, discussed in Chapter 9 and Chapter 11; for the purposes of this chapter, it operates as a conversion of selbri, similarly to the cmavo of selma'o SE. This conversion changes

10.7)    tu'a mi rinka
        le nu do morsi
    something-to-do-with me causes
        the event-of you are-dead
    My action causes your death.

10.8)    mi jai rinka le nu do morsi
    I am-associated-with causing the event-of your death.
    I cause your death.

In English, the subject of ``cause'' can either be the actual cause (an event), or else the agent of the cause (a person, typically); not so in Lojban, where the x1 of ``rinka'' is always an event. Example 10.7 and Example 10.8 look equally convenient (or inconvenient), but in making descriptions, Example 10.8 can be altered to:

10.9)    le jai rinka
        be le nu do morsi
    that-which-is associated-with causing
        (the event-of your death)
    the one who caused your death

The weakness of ``jai'' used in descriptions in this way is that it does not specify which argument of the implicit abstraction is being raised into the x1 place of the description selbri. One can be more specific by using the modal form of ``jai'' explained in Chapter 9:

10.10)  le jai gau rinka
        be le nu do morsi
    that-which-is agent-in causing
        (the event-of your death)

12. Event-type abstractors and event contour tenses

This section is a logical continuation of Section 3.

There exists a relationship between the four types of events explained in Section 3 and the event contour tense cmavo of selma'o ZAhO. The specific cmavo of NU and of ZAhO are mutually interdefining; the ZAhO contours were chosen to fit the needs of the NU event types and vice versa. Event contours are explained in full in Chapter 10, and only summarized here.

The purpose of ZAhO cmavo is to represent the natural portions of an event, such as the beginning, the middle, and the end. They fall into several groups:

The cmavo ``pu'o'', ``ca'o'', and ``ba'o'' represent spans of time: before an event begins, while it is going on, and after it is over, respectively.

The cmavo ``co'a'', ``de'a'', ``di'a'', and ``co'u'' represent points of time: the start of an event, the temporary stopping of an event, the resumption of an event after a stop, and the end of an event, respectively. Not all events can have breaks in them, in which case ``de'a'' and ``di'a'' do not apply.

The cmavo ``mo'u'' and ``za'o'' correspond to ``co'u'' and ``ba'o'' respectively, in the case of those events which have a natural ending point that may not be the same as the actual ending point: ``mo'u'' refers to the natural ending point, and ``za'o'' to the time between the natural ending point and the actual ending point (the ``excessive'' or ``superfective'' part of the event).

The cmavo ``co'i'' represents an entire event considered as a point-event or achievement.

For events seen as states and abstracted with ``za'i'', the meaningful event contours are the spans ``pu'o'', ``ca'o'', and ``ba'o''; the starting and ending points ``co'a'' and ``co'u'', and the achievement contour ``co'i''. States do not have natural endings distinct from their actual ending. (It is an open question whether states can be stopped and resumed.)

For events seen as activities and abstracted with ``zu'o'', the meaningful event contours are the spans ``pu'o'', ``ca'o'', and ``ba'o'', and the achievement contour ``co'i''. Because activities are inherently cyclic and repetitive, the beginning and ending points are not well-defined: you do not know whether an activity has truly begun until it begins to repeat.

For events seen as point-events and abstracted with ``mu'e'', the meaningful event contours are the spans ``pu'o'' and ``ba'o'' but not ``ca'o'' (a point-event has no duration), and the achievement contour ``co'i''.

Note that the parts of events are themselves events, and may be treated as such. The points in time may be seen as ``mu'e'' point-events; the spans of time may constitute processes or activities. Therefore, Lojban allows us to express processes within processes, activities within states, and many other complicated abstract things.

13. Abstractor connection

An abstractor may be replaced by two or more abstractors joined by logical or non-logical connectives. Connectives are explained in detail in Chapter 14. The connection can be expanded to one between two bridi which differ only in abstraction marker. Example 13.1 and Example 13.2 are equivalent in meaning:

13.1)    le ka la frank. ciska cu xlali
        .ije le ni la frank. ciska cu xlali
    The quality-of Frank's writing is bad,
        and the quantity of Frank's writing is bad.

13.2) le ka je ni la frank. ciska cu xlali
    The quality and quantity of Frank's writing is bad.

This feature of Lojban has hardly ever been used, and nobody knows what uses it may eventually have.

14. Table of abstractors

nu event of    fasnu       nun
        x1 is an event of (the bridi)
ka  property of ckaji       kam
        x1 is a property of (the bridi)
ni  amount of   klani       nil
        x1 is an amount of (the bridi)
            measured on scale x2
jei truth-value of  jetnu       jez
        x1 is a truth-value of (the bridi)
            under epistemology x2
li'i    experience of   lifri       liz
        x1 is an experience of (the bridi)
            to experiencer x2
si'o    idea of     sidbo       siz
        x1 is an idea/concept of (the bridi)
            in the mind of x2
du'u    predication of  -----       dum
        x1 is the bridi (the bridi)
            expressed by sentence x2
su'u    abstraction of  sucta       sus
        x1 is an abstract nature of (the bridi)
za'i    state of    zasti       zam
        x1 is a state of (the bridi)
zu'o    activity of zukte       zum
        x1 is an activity of (the bridi)
pu'u    process of  pruce       pup
        x1 is a process of (the bridi)
mu'e    point-event of  mulno       mub
        x1 is a point-event/achievement
            of (the bridi)

Please contact us with any comments, suggestions or concerns.